We propose a new ‘Mark-Ant-Walk’ algorithm for robust and efficient
covering of continuous domains by ant-like robots with very limited
capabilities. The robots can mark places visited with pheromone
marks and sense the level of the pheromone in their local neighborhood.
In the case of multiple robots, these pheromone marks can be
sensed by all robots and provide the only way of (indirect) communication
between the robots. The robots are assumed to be memoryless,
and to have no information besides that mentioned above. Despite the
robots’ simplicity we show that they are able, by running a very simple
rule of behavior, to ensure efficient covering of arbitrary connected
domains, including non-planar and multidimensional domains. The
novelty of our algorithm lies in the fact that, unlike previously proposed
methods, our algorithm works on continuous domains without
relying on some induced underlying graph effectively reducing the
problem to a discrete case of graph covering. In addition, we demonstrate
various benefits of our algorithm such as ability to cope with
arbitrary initial pheromone profile and a bounded constant time between
two successive visits of the robot at the same location, making
it suitable for patrolling. Finally, we provide a new theoretical bound
on covering time of a wide family of such mark and walk algorithms.